The Quinnipiac University/New York Times/CBS poll shows Obama with 51 percent of those surveyed to 46 percent for Romney, The New York Times reported.
Ron Jankowski, 39, of Racine, is one of 3 percent who said they have not made up their minds.
He told the Times he voted for Obama four years ago, and is open to changing -- but does not think Romney has made his case yet.
"Obama is putting out his plans and his details and being more public on that, but with Romney it's kind of gray," Jankowski said. "I'd like to know more -- educate me."
The survey found women are far more likely to support Obama than men are to back Romney. While 55 percent of the women surveyed backed the president and 41 percent Romney, Romney led among men by only 2 percentage points.
Wisconsin has 10 electoral votes and has become an important state for Romney to carry, given his lag in some major swing states, the Times said. His vice-presidential choice, Paul Ryan, represents the state in Congress and Republican Gov. Scott Walker fought off a recall this year, but that does not appear to be helping Romney, the report said.
The shows Democrat Tammy Baldwin tied with Republican Tommy Thompson, 47-47, in the Wisconsin U.S. Senate race.
Quinnipiac conducted telephone interviews of 1,485 likely voters in Wisconsin Sept. 11-17. The overall margin of sampling error was 3 percentage points.
Notable deaths of 2014 [PHOTOS]